The GATE Grind

GATE 2025 CH – Question 22

Mass Transfer · Mass transfer theories and momentum, heat and mass transfer analogies · 1 mark · Multiple choice

If $k$ is the mass transfer coefficient and $D_v$ is the molecular diffusivity, which one of the following statements is NOT CORRECT with respect to mass transfer theories?

  1. For Film theory, $k \propto D_v$
  2. For Penetration theory, $k \propto D_v^{1/3}$
  3. For Surface Renewal theory, $k \propto D_v^{1/2}$
  4. For Boundary Layer theory, $k \propto D_v^{2/3}$

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Correct answer: (B) For Penetration theory, $k \propto D_v^{1/3}$

Explanation

The film theory gives $k = D_v/\delta$, so $k \propto D_v$. The penetration theory gives $k = 2\sqrt{D_v/(\pi t_c)}$, and the surface renewal theory gives $k = \sqrt{D_v s}$, so both vary as $D_v^{1/2}$. The boundary layer theory gives $k \propto D_v^{2/3}$ (through $Sc^{-2/3}$). So the statement for the penetration theory, with the power 1/3, is the one that is not correct.